H.
Caprasse, Institut de Physique B-5, Sart-Timan, B-4000 LIEGE
1

Computer algebra is seen from the point of view of APPLICATIONS in fundamental physics. Especially in Cosmology, General Relativity, Particle Physics and Field Theory. These applications have been done mostly with the package REDUCE are at the origin of several extensions working on top of it. These extensions are conceived in such a way that their range of applicaility goes far beyond the types of problems which have suggested them.

Three packages have been developed either alone or in collaborations. Their are :

- ASSIST: which provides a large number of additional functionalities to the kernel of REDUCE.
- DUMMY which makes the system capable to handle
**dummy variables**and to simplify generic polynomial expressions which contain dummy summations. - CANTENS which makes REDUCE able to handle i
**ndexed objects**such as tensors and fields.

These packages are compatible. DUMMY needs ASSIST to work properly and CANTENS needs both ASSIST and DUMMY.

Computer algebra is taught mainly to physics student interested in theoretical physics. It is based on a book written in french recently edited by HERMES under the title

`Calcul formel
et manipulations qcdiques`

References : **ISBN 2-86601-658-0**

** ISSN
0993-5037**

The table of content is available.

**News: **

The latest versions of ASSIST
DUMMY and
CANTENS
are available. The package **CANTENS** is the newest
one and is still subjected to frequent updatings. It exploits and
extends the capabilities of **DUMMY **to find normal forms for polynomial
expressions involving dummy summations. It allows to handle indexed
objects of various kinds such as

**tensors, spinors, Poisson
and Lie algebra generators ,**

**classical and quantum
fields.**

Moreover, it is the only one we know in the world
which can work * simultaneously *within several (sub-)spaces. Tensor
contractions involving invariant tensors such as delta , epsilon and also
involving metric tensors are automatically made applying when the key function

compiled versions of these packages for Windows3.x and Win95 are also available.

Any further inquiries can be mailed to

General Informations on Computer Algebra Systems and Activities:

The SAC Newsletter gives many and various informations on the pedagogical , scientific and applied aspects of computer algebra.

OPENMATH is a standard to communicate
mathematical objects between various programming environmenents and applications.
The site contain a list of workgroups interested in the manipulation of
mathematical objects .

**General informations on MATHEMATICA**: MATHEMATICA

**General informations on MAPLE:** MAPLE

**General informations on MuPAD: **MuPAD

Do you want to make a**
calculation **with**
REDUCE ?**

Do you want to **test**
**REDUCE ?**

**IMACS-ACA conferences of 1998 and
1999 **

Physique Théorique

Institut d'Astrophysique et de
Géophysique

Tel: (32-4) 366 36 04